Questions tagged [renormalization]
This tag is for questions which relates with the renormalization, an ensemble of techniques which serves to treat the infinities which appear in quantum field theory or statistical mechanics. Renormalization procedures are based on the requirement that certain physical quantities (such as the mass and charge of an electron) equal observed (experimental) values.
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$\phi^4$ quantum fields theory with vanishing physical mass
Let us consider the $\phi^4$ theory, where $\phi$ is a real scalar field, such that the physical mass vanishes.
Is it true that the bare mass also vanishes?
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QED with massless fermions
Consider QED such that physical mass of fermions vanishes. Is it true that their bare mass also vanishes?
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Confusion about solution of the Callan-Symanzik Equation
In the QFT textbook by Peksin and Schroeder, they apply a hydrodynamic-bacteriological analogy to derive the solution of the Callan-Simanzik equation. Yet I'm confused with the integration boundary on ...
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Beta function calculation in massless minimal subtraction $\phi^4$ theory
I'm trying to understand how to calculate the beta function in massless phi^4 theory using dimensional regularisation and minimal subtraction. I'm struggling to understand:
Is it possible to ...
CommunityBot
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QFT with massless particles
EDIT: Often in textbooks one discusses QFT with massless particles, e.g. massless fermions or scalar particles. What mass vanishes: bare or physical? or both?
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Missing counterterms in $\phi^3$ + $\phi^4$ theory in 1PI effective action
I hope I'm just overlooking something. The Lagrangian is as follows:
$$\mathcal{L}=\frac{1}{2}(\partial_\mu \phi)^2-(\frac{1}{2}m^2\phi^2+\frac{1}{3!}g\phi^3+\frac{1}{4!}\lambda\phi^4)$$
and I just ...
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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]
In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]
I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here.
In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
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What does it mean to "resum" the large logarithms?
I am struggling to understand the concept of resummation of large logarithms in QFT; from what I learnt so far the problem relies on the fact that if a full theory defined in the UV contains much ...
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$\operatorname{O}(N)$ sigma model at large $N$
I would like to better understand the main principles of large-$N$ expansion in quantum field theory. To this end, I decided to consider a simple toy model with lagrangian (from Wikipedia)
$
\mathcal{...
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Universality and continuous variation of critical exponent close to a tricritical point
A tricritical point is a point at which a second order transition line and a first order transition line merge.
At equilibrium, this point can be described by a landau potential (see for example this ...
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Role of the natural temperature scale in the anomalous dimension of the renormalization group
In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
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Asymptotic Freedom QCD
I'm trying to understand the derivation of asymptotic freedom with the renormalisation group equations. I'm reading Taizo Muta's book on QCD. What I don't understand is how he obtains the last ...
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Trouble with the algebra in Srednicki book chapter 28
I'm studying chapter 28 in Srednicki (the renormalization group) and I'm having troubles figuring out how he derives eq. (28.15) (last summation above) from eqs. (28.7) and (28.9).
More specifically ...
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Canonical commutation relation in QFT
The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is
$$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$
Is this equation satisfied by ...
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